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Chapter 1: INTRODUCTION
1. Evolution of Wireless Technologies
At the beginning of 2001, more than one out of 10 people in the world had a mobile
telephone. The end-user equipment size, weight, and costs have dropped over 20% per year over
the past 15 years. This incredible growth in the industry is due to the development of wireless
communication technologies.
The first generation wireless communication system was the analog advanced mobile
phone system (AMPS), developed primarily by AT & T. This system used a 30 kHz channelspacing while narrowband AMPS (N-AMPS), which was developed by Motorola, worked within a
10 kHz channel spacing thus increasing the AMPS capacity. The frequency division multiple
access (FDMA) systems divide a wide frequency band into smaller frequency bands that are
assigned to specific users allowing different users to communicate at the same time.
These first generation systems had capacity limitations since each spectral channel could be
allocated to only one user. Because of the capacity limitations of the FDMA based analog cellular
systems, the first digital cellular systems were based on time division multiple access (TDMA).
TDMA systems divide their signals into shorter time slots thus allowing several mobile telephones
to communicate on a single radio carrier frequency. The digital AMPS (D-AMPS) was developed
in the late 1980s which was followed by the first Groupe Special Mobile (GSM) deployments.
Today, it is estimated that there are over 800 million GSM subscribers across the 190 countries of
the world. These TDMA systems come under the second generation cellular systems. Figure shows
the evolution of wireless technologies in various stages.
Spread spectrum technology, which was initially used in military applications, is another
approach to achieve multiple access. In it, a narrowband signal is spread over a wide frequency
band for transmission using code division multiple access (CDMA); it is also called spread
spectrum multiple access (SSMA).
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Figure1.1 Evolution of Wireless Technologies
CDMA was pioneered and commercially developed by QUALCOMM in 1995. In it,
multiple users can share the radio channel at the same time. The frequency reuse limitations in
FDMA and TDMA are less in CDMA and so CDMA is an attractive alternative to GSM.
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Figure 1.2 Various Multiple Access Technologies
The international telecommunications union (ITU) undertook the international mobile
telephony-2000 (IMT-2000) project and developed the third generation systems. The primary third
generation technologies which were approved by ITU in 1998 were :
Wideband CDMA (W-CDMA), developed by the European telecommunication standardization
institute (ETSI).
Cdma2000, developed by the telecommunications industry association (TIA).
EDGE (Enhanced Data Rates for GSM Evolution) which was co-sponsored by ETSI and the
TIA.
As the wireless personal communications field has grown over the last few years, the
method of communication known as spread spectrum has gained a great deal of prominence.
Spread spectrum involves spreading the desired signal over a bandwidth much larger than the
minimum bandwidth necessary to send the signal. It was originally developed by the military as a
method of communications that is less sensitive to intentional interference or jamming by third
parties, but has become very popular in the realm of personal communications recently. Spread
spectrum methods can be combined with Code Division Multiple Access (CDMA) methods to
create multi-user communications systems with very good interference performance.
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Chapter 2: Spread Spectrum Communication
Systems
2.1 Introduction
Spread spectrum signals for digital communications were originally developed and used for
military communications either (l) to provide resistance to hostile jamming, (2) to hide the signal
by transmitting it at low power and, thus, making it difficult for an unintended listener to detect its
presence in noise, or (3) to make it possible for multiple users to communicate through the same
channel. Today, however, spread spectrum signals are being used to provide reliable
communications in a variety of commercial applications, including mobile vehicular
communications and interoffice wireless communications.
As stated before, spread spectrum systems afford protection against jamming (intentional
interference) and interference from other users in the same band as well as noise by spreading
the signal to be transmitted and performing the reverse de-spread operation on the received
signal at the receiver. This de-spreading operation in turn spreads those signals which are not
properly spread when transmitted, decreasing the effect that spurious signals will have on the
desired signal. Spread Spectrum systems can be thought of as having two general properties: first,
they spread the desired signal over a bandwidth much larger than the minimum bandwidth needed
to send the signal, and secondly, this spreading is carried out using a pseudorandom noise (PN)
sequence. In a general sense, we will see that the increase in bandwidth above the minimum
bandwidth in a spread spectrum system can be thought of as applying gain to the desired signal
with respect to the undesirable signals. We can now define the processing gain GPas
inf
RF
P
o
BWG
BW=
Where BWRF is the bandwidth that the signal has been increased, and BWinfo is the minimum
bandwidth necessary to transmit the information or data signal. Processing gain can be thought of
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as the improvement over conventional communication schemes due to the spreading done on the
signal. Often, a better measure of this gain is given by thejamming margin,
m i n( ) ( )J P M d B G d B=
Which indicates the amount of interference protection offered before the signal is corrupted.
The spreading function is achieved through the use of a pseudorandom noise sequence (PN
sequence). The data signal is combined with the PN sequence such that each data bit is encoded
with several if not all the bits in the PN sequence. In order to achieve the same data rate as was
desired before spreading, the new data must be sent at a rate equal to the original rate multiplied by
the number of PN sequence bits used to encode each bit of data. This increase in bandwidth is the
processing gain, which is a measure of the noise and interference immunity of this method of
transmission.
To see how the spreading process helps protect the signal from outside interference, let us
look at the types of interference that are possible. The three major types of interference that can
arise when using wireless networks are: (1) noise, (2) intentional interference from a jammer or
other source trying to disrupt communications, and (3) unintentional interference from other users
of the same frequency band. Noise can be considered as background white Gaussian noise (WGN),
and can be said to have power spectral density N0. Since the noise is white, the spreading of the
bandwidth does not have much of an effect here. The noise power is constant over the entire
bandwidth, so increasing the bandwidth actually lets more noise into the system, which might be
seen as detrimental. However, we will see that this is not really a problem.
Intentional interference comes from sources who are actively trying to corrupt the data
transmission by sending power transmissions in the same band as the intended transmission. The
big difference between intentional interference and noise is that intentional interference is, by its
very nature, a finite power signal, since it must be transmitted from a real source. Thus the
spreading performed on the data signal allows the signal to hide itself in a larger bandwidth,
forcing the jamming signal to distribute its power over this new much larger bandwidth, and thus
intuitively diminishing the effect that the jamming signal has on the data signal.
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The third major source of signal corruption comes from unintentional interference due to
other users using the same frequency band, and here, the system uses the PN sequence and the
technique of CDMA to combat this type of interference. In a wireless communications network, all
the signals propagate through the air by way of electromagnetic waves, thus there is no way to
ensure that one user will receive only the signal he or she desires; that user will receive all the
signals being sent in that band. By giving each of the signals to be transmitted in the frequency
band its own code (CDMA) which is orthogonal to the other codes used in that band, the effect of
these other signals will effectively be zero at the receiver (when the receiver correlates the input
signal it receives with the code of the transmission it wants to receive, only the desired signal will
Remain). The following sections will analyze and derive the specifics of the two major types of
spread spectrum systems, Direct Sequence and Frequency Hop. Since the mechanisms by which
the above advantages are achieved vary between the two methods, the analysis has been left until
those sections.
The basic elements of a spread spectrum digital communication system are illustrated in
Figure 2.1. We observe that the channel encoder and decoder and the modulator and demodulator
are the basic elements of a conventional digital communication system' In addition to these
elements, a spread spectrum system employs two identical pseudorandom sequence generators, one
of which interfaces with the modulator at the transmitting end and the second of which interfaces
with the demodulator at the receiving end' These two generators produce a pseudorandom or
pseudo noise(PN) binary-valued sequence that is used to spread the transmitted signal in frequency
at the Inoculators to dispread the received signal at the demodulator. Time synchronization of the
PN sequence generated at the receiver with the PN sequence Contained in the received signal is
required to properly dispread the received spreads spectrum signal. In a practical system,
synchronization is established prior to the transmission of information by transmitting a fixed PN
bit pattern that is designed so that the receiver will detect it with high probability in the presence of
interference. After time synchronization of the PN sequence generators is established, thetransmission of information commences. In the data mode, the communication system usually
tracks the timing of the incoming Received signal and keeps the PN sequence generator in
synchronism.
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Figure 2.1 spread spectrum digital communication system
There are two basic types of spread spectrum signals for digital communications namely direct
sequence (DS) spread spectrum and frequency_ hopped (FH) spread spectrum
2.2 Direct Sequence Spread Spectrum
In telecommunications, direct-sequence spread spectrum (DSSS) is a modulation
technique. As with other spread spectrum technologies, the transmitted signal takes up more
bandwidth than the information signal that is being modulated. The name 'spread spectrum' comes
from the fact that the carrier signals occur over the full bandwidth (spectrum) of a device's
transmitting frequency.
2.2.1 Features
It phase-modulates a sine wave pseudo randomly with a continuous string of pseudo noise
(PN) code symbols called "chips", each of which has a much shorter duration than an information
bit. That is, each information bit is modulated by a sequence of much faster chips. Therefore, the
chip rate is much higher than the information signal bit rate. It uses a signal structure in which the
sequence of chips produced by the transmitter is known a priori by the receiver. The receiver can
then use the same PN sequence to counteract the effect of the PN sequence on the received signal
in order to reconstruct the information signal.
2.2.2 Transmission method for DSSS
Direct-sequence spread-spectrum transmissions multiply the data being transmitted by a
"noise" signal. This noise signal is a pseudorandom sequence of 1 and 1 values, at a frequency
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much higher than that of the original signal, thereby spreading the energy of the original signal into
a much wider band as shown in figure 2.2. The resulting signal resembles white noise, like an
audio recording of "static". However, this noise-like signal can be used to exactly reconstruct the
original data at the receiving end, by multiplying it by the same pseudorandom sequence (because
1 1 = 1, and 1 1 = 1). This process, known as "de-spreading" as shown in figure 2.3,
mathematically constitutes a correlation of the transmitted PN sequence with the PN sequence that
the receiver believes the transmitter is using.
For de-spreading to work correctly, the transmit and receive sequences must be
synchronized. This requires the receiver to synchronize its sequence with the transmitter's
sequence via some sort of timing search process. However, this apparent drawback can be a
significant benefit: if the sequences of multiple transmitters are synchronized with each other, the
relative synchronizations the receiver must make between them can be used to determine relative
timing, which, in turn, can be used to calculate the receiver's position if the transmitters' positions
are known. This is the basis for many satellite navigation systems.
Figure 2.2 Generation of Spreading Sequences
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The resulting effect of enhancing signal to noise ratio on the channel is called process gain.
This effect can be made larger by employing a longer PN sequence and more chips per bit, but
physical devices used to generate the PN sequence impose practical limits on attainable processing
gain.
Figure 2.3 Generation of De-spreading Sequences
If an undesired transmitter transmits on the same channel but with a different PN sequence
(or no sequence at all), the de-spreading process results in no processing gain for that signal. This
effect is the basis for the code division multiple access (CDMA) property of DSSS, which allows
multiple transmitters to share the same channel within the limits of the cross-correlation properties
of their PN sequences.
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Systems using DS-SS require more bandwidth and this contradicts the concept of
bandwidth conservation. However, many advantages exist to using such a system. The
development of DS-SS was conducted for the military, so the most advantageous facet is the
inherent security of the system. The PN sequence encodes the data making it difficult to intercept
and decode the signal without knowing the coded sequence used. The spreading process also
makes jamming the signal difficult because the jamming signal is spread during the despreading
process. Thus reducing its effect on the transmitted signal.
Because each signal is encoded with a unique PN sequence, multiple signals can be
transmitted within the same frequency band. Code Division Multiple Access (CDMA) uses spread
spectrum technology and each transmitter uses a different spreading code to allow for multiple
transmissions over the same channel. This property of the CDMA method of transmission has
increased the popularity of this type of wireless communication. The CDMA method is widely
used in current wireless systems and its use in next generation systems is anticipated. In GPS, each
satellite transmits data that has been spread by a PN sequence. All satellites transmit independently
using different spreading codes in the same frequency band so the system is classified as CDMA.
2.3 Frequency Hopped Spread Spectrum
Frequency hopping is one of two basic modulation techniques used in spread spectrum
signal transmission. In frequency hopped spread spectrum the available channel bandwidth W is
subdivided into a large number of non-overlapping frequency slots. In any signaling interval the
transmitted signal occupies one or more of the available frequency slots. The selection of the
frequency slot in each signal interval is made pseudo randomly according to the output from a PN
generator. It is the repeated switching of frequencies during radio transmission, often to minimize
the effectiveness of "electronic warfare" - that is, the unauthorized interception or jamming of
telecommunications. It also is known as frequency- hopping code division multiple access ( FH-
CDMA). Spread spectrum modulation techniques have become more common in recent years.
Spread spectrum enables a signal to be transmitted across a frequencyband that is much wider than
the minimumbandwidth required by the information signal. The transmitter "spreads" the energy,
originally concentrated in narrowband, across a number of frequency band channels on a wider
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electromagnetic spectrum. Benefits include improved privacy, decreased narrowband interference,
and increased signal capacity.
In an FH-CDMA system, a transmitter "hops" between available frequencies according to a
specified algorithm, which can be either random or preplanned. The transmitter operates in
synchronization with a receiver, which remains tuned to the same center frequency as the
transmitter. A short burst of data is transmitted on a narrowband. Then, the transmitter tunes to
another frequency and transmits again. The receiver thus is capable of hopping its frequency over a
given bandwidth several times a second, transmitting on one frequency for a certain period of time,
then hopping to another frequency and transmitting again. Frequency hopping requires a much
wider bandwidth than is needed to transmit the same information using only one carrier frequency.
The spread spectrum approach that is an alternative to FH-CDMA is direct sequence code divisionmultiple access (DS-CDMA), which chops the data into small pieces and spreads them across the
frequency domain. FH-CDMA devices use less power and are generally cheaper, but the
performance of DS-CDMA systems is usually better and more reliable. The biggest advantage of
frequency hopping lies in the coexistence of several access points in the same area, something not
possible with direct sequence.
Certain rules govern how frequency-hopping devices are used. In North America, the Industrial,
Scientific, and Medial (ISM) waveband is divided into 75 hopping channels, with power
transmission not to exceed 1 watt on each channel. These restrictions ensure that a single device
does not consume too much bandwidth or linger too long on a single frequency.
2.3.1 Features
FHSS is one of two types of spread spectrum radio, the other being direct-sequence spread
spectrum. FHSS is a transmission technology used in wireless transmissions where the data signal
is modulated with a narrowband carrier signal that "hops" in a random but predictable sequence
from frequency to frequency as a function of time over a wide band of frequencies. The signal
energy is spread in time domain rather than chopping each bit into small pieces in the frequency
domain. This technique reduces interference because a signal from a narrowband system will only
affect the spread spectrum signal if both are transmitting at the same frequency at the same time. If
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synchronized properly, a single logical channel is maintained. The transmission frequencies are
determined by a spreading, or hopping, code. The receiver must be set to the same hopping code
and must listen to the incoming signal at the right time and correct frequency in order to properly
receive the signal. Current FCC regulations require manufacturers to use 75 or more frequencies
per transmission channel with a maximum dwell time (the time spent at a particular frequency
during any single hop) of 400 ms.
The overall bandwidth required for frequency hopping is much wider than that required to
transmit the same information using only one carrier frequency. However, because transmission
occurs only on a small portion of this bandwidth at any given time, the effective interference
bandwidth is really the same. Whilst providing no extra protection against wideband thermal noise,
the frequency-hopping approach does reduce the degradation caused by narrowband interferers.One of the challenges of frequency-hopping systems is to synchronize the transmitter and receiver.
One approach is to have a guarantee that the transmitter will use all the channels in a fixed period
of time. The receiver can then find the transmitter by picking a random channel and listening for
valid data on that channel. The transmitter's data is identified by a special sequence of data that is
unlikely to occur over the segment of data for this channel and the segment can have a checksum
for integrity and further identification.
2.3.2 Transmission method for FHSS
A block diagram of the transmitter and receiver for a FH spread spectrum system is shown in
Figure 2.4 The modulation is either binary or M-ary FSK. For example if binary FSK is employed,
the modulator selects one of two frequencies, f0 or f1 corresponding to the transmission of a0 for
a1. The resulting binary FSK signal is translated in frequency by an amount that is determined by
the output sequence from PN generator which is used to select a frequency fc that is synthesized by
the frequency synthesizer. This frequency-translated signal is transmitted over the channel. For
example, by taking m bit form the PN generator, we may specify possible carrier frequencies.
At the receiver, there is an identical PN sequence generator, synchronized with the received
signal, which is used to control the output of the frequency synthesizer. Thus the pseudorandom
frequency translation introduced at the transmitter is removed at the demodulator by mixing the
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synthesizer output with the received signal. The resultant signal is then demodulated by means of
an FSK demodulator, a signal for maintaining synchronism of the PN sequence generator with the
FH received signal is usually extractor form the received signal.
Figure 2.4 frequency hopped spread spectrum system
Although binary PSK modulation generally yield better performance than FSK , it is
difficult to maintain phase coherence in the synthesis of the frequencies used in the hopping pattern
and, also, in the propagation of the signal over the channel as the signal is hopped from one
frequency to another over a wide bandwidth. Consequently, FSK modulation with non-coherent
demodulation is usually employed in FH spread spectrum systems. The frequency hopping rate,
denoted as Rh, may be selected to be either equal to the symbol rate, lower than the symbol rate, or
higher than the symbol rate. If Rh is equal to lower part at the symbol rate, the FH system is called
a slow hopping system. If Rh is higher that symbol rate, the FH system is called a fast hopping
system
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2.4 CDMA
Time division multiple access (TDMA) and frequency division multiple access (FDMA)
are commonly used multiple access communications systems. TDMA communications use theentire bandwidth to which it is assigned and separates each user by assigning a repetitive time
interval. The user can only communicate in the assigned time slots. This TDMA approach is
inefficient because, during idle times, communications do not use that portion of the fixed timeslot
for operation. In FDMA communications, each user is assigned a frequency slot in the
communication bandwidth in which to communicate. This FDMA approach is inefficient because,
during idle times, communications do not require that portion of the bandwidth for operation.
TDMA also requires synchronization overhead to maintain the operational performance of the
system. In the FDMA system, imperfect band-pass filters exist, requiring frequency slots to be
separated by guard bands to prevent interference from adjacent frequency slots.
The enhancement in performance obtained from a DS spread spectrum signal through the
processing gain and the coding gain can be used to enable many DS spread spectrum signals to
occupy the same channel bandwidth, provided that each signal has its own pseudorandom
sequence, thus it is possible to have several users transmit message simultaneously over the same
channel bandwidth. This type of digital communication, in which each transmitter/receiver user
pair has its own distinct signature code for transmitting over a common channel bandwidth, is
called code division multiple access.
In digital cellular communications, a base station transmits signal to number of mobile
receivers using orthogonal PN sequence, one for each intended receiver, these signals are perfectly
synchronized at transmission, so that they arrive at each mobile receiver in synchronism.
Consequently, due to the orthogonality of the number of PN sequence, each intended receiver can
demodulate its own signal without interference from the other transmitted signals that share the
same bandwidth. However, this type of synchronism cannot be maintained in the signals
transmitted from the mobile transmitters to the base station. In the demodulation of each DS spread
spectrum signal at the base station, the signals from the other simultaneous users of the channel
appear as additive interference. Let us determine the number of simultaneous signals that can be
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accommodated in a CDMA system. We assume that all signals have identical average powers at
the base station. In many practical system the received signals power level from each user is
monitored at the base station, and power control is exercised over all simultaneous users by use of
a a control channel that instructs the users on whether to increase or decrease their power levels.
The advantage of the CDMA method over the other methods is that instead of isolating
each user, all users share the channel resources. Each user is assigned a unique PN sequence with
which to encode and decode the data. They all transmit on the same carrier frequency with
approximately the same power level that is below the background noise level. The PN sequences
used in the system have low cross-correlations with each other, and therefore, interference with
other signals is low. GPS uses a PN sequence called Gold Sequences, which are a class of low
cross-correlation codes. This approach makes each user seem as though they are operating alone
within a channel of high background noise. This allows systems using CDMA to accommodate a
large number of users within the same bandwidth and no part of the system is reserved for idling
users. The receiver will synchronize with the desired signal bringing the power of that data signal
above the background noise. This process works despite the fact that the signals all transmit on the
same bandwidth and at approximately the same power level. GPS signals utilize CDMA
communications using direct sequence bi-phase modulation of the carrier frequency. From any
location on the surface of the earth, five to twelve GPS satellites are typically visible at any given
time. Demodulation of the CDMA signals transmitted provides a spreading gain that renders the
power level of the signal above that of the background noise level.
Chapter 3: PN-sequences
3.1 Generation of PN sequences
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On the basis of what has been said of the DS spread-spectrum system that is the core of the
CDMA system, we can state that CDMA is an MA technique that uses spread-spectrum
modulation by each accessing party with its own unique spreading code, with all accessing parties
sharing the same spectrum. It is also clear now that spread-spectrum modulation is accomplished
by means of PN codes. The narrowband information signal or information sequence is modulated
(multiplied) by the wideband spreading signal (sequence), thereby spreading the information signal
spectrum to a substantially greater bandwidth prior to transmission. It is important to recognize
that CDMA can only be accomplished by spread-spectrum modulation, while spread-spectrum
modulation does not mean CDMA.
Pseudorandom or pseudonoise (PN) sequences are used in data scrambling in the IS-95
system as well as for spread-spectrum modulation. Data scrambling is achieved by changing the
data sequence "randomly" or in a noise-like fashion before transmission. At the receiver, the
scrambled sequence is "changed back" to the original data sequence. The two concepts,
"randomness" and "changing back," are the key ideas involved in understanding the CDMA
system. If the generated sequence were completely random, the receiver would have no way to
change back. On the other hand, if the receiver knows how to change back, the sequence cannot be
completely random.Consider the following sequences:
Data sequence 1 1 0 0 1 0 1 0 0 1 0 1 0 1...
Random sequence 1 0 1 0 0 0 0 1 0 1 1 0 1 0...
Transmitted sequence 0 1 1 0 1 0 1 1 0 0 1 1 1 1...
The transmitted sequence is a scrambled version of the data sequence obtained by the bit-
by-bit modulo-2 addition of the data sequence and a random sequence. At the receiver, an identical
"random" sequence is added to the received sequence, which in the absence of noise is the
transmitted sequence:
Transmitted sequence 0 1 1 0 1 0 1 1 0 0 1 1 1 I...
Random sequence 1 0 1 0 0 0 0 1 0 1 1 0 1 0.. .
Data sequence 1 1 0 0 1 0 1 0 0 1 0 1 0 1.. .
This illustration reveals two fundamental requirements on the random sequence:
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It must be reproducible at the receiver;
It must be reproduced in synchronism with the scrambling sequence at the transmitter.
These two requirements make it virtually impossible to use a completely random sequence and
hence, in practice, we use a sequence that has sufficient randomness to be unrecognizable to
unintended receivers and yet is deterministic to make it relatively easy to generate and to
synchronize at the receiver.
The most important method of generating such binary sequences is by means of a linear
feedback shift register (LFSR). For an LFSR sequence generator with n stages, the output sequence
will always be periodic because, whatever the initial conditions of the shift register, after a finite
number of clock pulses, the initial conditions must eventually be reproduced. Because the
maximum number of different combinations of n binary digits is 2n , the period cannot exceed 2n .
Because the all-zero condition, if reached, remains in the same state forever, it cannot appear in the
shift register if the initial condition (initial loading or state) is not all zeros. Therefore, the
maximum number of possible states is 2 1n .
A shift register output sequence with the period 2 1n is called a "maximal length
sequence" or "m-sequence" for short. M-sequences are also referred to as "pseudorandom
sequences" or PN sequences. When PN sequences clocked at very high rates are modulated
(multiplied) with data sequences in a communications system, such as the IS-95 system, it is a
spread spectrum system that provides 10 log (RN/Rb ) dB of "processing gain," where RN is the
PN sequence rate and Rb is the data rate.
The generation of PN sequences is accomplished using a linear feedback shift register
(LFSR)as shown in figure 2.5. In either case, the shift register generator is a finite-state machine
mechanized by a polynomial given in the form of
1 2 1
1 2 1( ) 1n n
ng D D s D s D s D
= + + + + + (1.1)
The polynomial (1.1) is a special type of polynomial, well tabulated in the literature, called
an generator polynomial, which specifies a set of nonzero coefficients {si), where si = 1 denotes a
connection and = 0 denotes the lack of a connection in the mechanization of the LFSR
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configuration. The sequences generated by such an LFSR with an initial loading of nonzero n-
tuples in the n stages, are periodic sequences with length N = 2 1n , and there are P different
sequences of length P that are shifted versions of the given initial sequence of length P. The
sequences generated in this way are the ones used. There are three most important properties
associated with a PN sequence, aside from the basic property that it has the maximal length of
2 1n , where n is the number of stages of the LFSR. Two of the three remaining properties have to
do with the randomness of the sequence, but the one we wish to mention here is the correlation
property. What it means is that if a complete sequence of length 2 1n is compared, bit by bit, with
any shift of itself (one of 2 1n remaining sequences), the number of agreements differs from the
number of disagreements by at most 1. This means that when two identical sequences are
compared, bit by bit, the number of agreements minus the number of disagreements is equal to the
number of agreements, which is 2 1n .
We generate the m-sequence using a Linear Feedback Shift Register (LFSR). The LFSR is
implemented in the modular format as shown below in Figure 3.1.
Figure3.1 Linear Feedback Shift Register
The modular format is suited for efficient hardware implementation and is faster compared to a
simple format. The initial load of the register, 1 2 3 1 0[ , , , , , ]n n nr r r r r r = cannot be in the all zero
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state and the generator polynomial taps , 1 2 3 1 0[ , , , , , ]n n n ng g g g g g g = should be such that 0g
and ng are non zero. If the initial load is the all-zero state, the registerr cannot update to any other
state and will result in zero output all the time. The elements of g and r are from the binary set
{0,1}. In Figure 1, the tap 0g =1 and represents the connection from the LSB 0r of the register to all
other generator taps. During a clock tick, the value in 0r is clocked out as the first output bit d. In
hardware implementation, the binary value in g determines the presence or absence of a modulo 2
multiplier. In MATLAB implementation, we AND (modulo 2 multiply) 0r with ng through 1g to
obtain , 1 2 3 1[ , , , , ]n n n ns s s s s s = as shown in Figure 3.1. Next we update the register r. We XOR
(modulo 2 addition) the vectors 1, 2 3 1[ , , , ]n n ns s s s and 1, 2 3 1[ , , , ]n n nr r r r and store the result in
2, 3 4 0[ , , , ]
n n nr r r r
. Finally, the MSB of the registerr, 1nr , is updated with the value of ns . The
register r is now next state and during the next clock cycle, the LSB 0r is clocked out as next
output of the m-sequence and the process continues. Here, n denotes the size of the linear feedback
shift register. The length of generated m-sequence is N= 2 1n and it repeats with period N.
3.2 Properties of Maximal Length PN Sequences
The maximal length PN sequences or m-sequences generated have many of the same
properties of a truly random sequence. A truly random sequence has an equal probability of a 1 or
a 0 occurring and the PN sequences come close to that property.
The properties of m-sequences are:
1. The Balance Property: The number of 1s in the sequence is always one greater than the number
of 0s.
2. The Shift and Add Property: The Modulo-2 addition of an m-sequence with a time-shiftedversion of the same m-sequence yields a second time-shifted version of the same m-sequence.
3. The Correlation Property: When a full period of an m-sequence is compared with a time-shifted
version of itself, the number of mismatched chips will exceed the number of matched chips by one.
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3.3 The Cross-Correlation Problem
The cross-correlation function between two distinct pseudorandom sequences is a very
important consideration in MA communications systems where each user terminal (access
terminal) is assigned a PN generator whose polynomial is distinct from all other user terminals. In
fact, this is the type of CDMA spread-spectrum system used by the military. A distinction between
the military type of CDMA system and the nonmilitary type such as IS-95 is that, in the former, the
communications channel condition does not permit a phase coherent PN code MA system, as
opposed to the more controllable channel conditions of cellular or PCS applications in which
mobilility is not a panicular concern. In a military or high-mobility environment, where the carrier
phase tracking is of insurmountable difficulty, a CDMA system based on a single PN code
generator, such as the IS-95 system, is not possible. The problem of assigning code generators with
low cross-correlation peaks is an important consideration.
For CDMA applications, m-sequences are not optimal. The m-sequences have excellent
autocorrelation properties but their cross-correlation properties do not follow any particular rules
and typically exhibit undesirably high values. For CDMA, we need to construct a family of
spreading sequences, one for each which, in which the codes have well-defined cross-correlation
properties. In general, m-sequences do not satisfy the criterion. One popular set of sequences thatdoes are the Gold sequences. Gold sequences are attractive because only simple circuitry is needed
to generate a large number of unique codes. A Gold sequence is constructed by the XOR of two m-
sequences with the same clocking. Gold sequences are generated from two equal length m-
sequences that form a so called preferred pair. To achieve increased capacity, at an expense of
altering the correlation properties slightly, a pair of m-sequences may be used to generate a set of
Gold sequence.
To overcome the cross-correlation problem, Gold considers the bit-by- bit modulo-2 sum
of two pseudorandom sequences of the same length but generated by two distinct primitive
polynomials. If the length of the two PN sequences is P = 2 1n , then the resultant sequence also
repeats itself after P bits. Further, if one sequence is kept fixed and the second sequence is shifted
in time, a different resultant sequence is generated. In this way, P different sequences can be
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generated, one for each different time shift of the second sequence. Joining the two original PN
sequences, altogether 2 1n + different sequences can be generated with one pair of primitive
polynomials. These sequences are referred to as Gold sequences or Gold codes; they are not
maximal except for the two original PN sequences.
Chapter 4: Gold Code Sequences
4.1Gold Code Generation
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The usefulness of the pseudorandom sequences in a spread-spectrum system depends in
large part on their ideal autocorrelation properties. One of the randomness properties of the
pseudorandom sequence is the correlation property; that is, if a complete sequence is compared, bit
by bit, with any shift of itself, the number of agreements differs from the number of disagreements
by at most one. The cross-correlation function between two different pseudorandom sequences of
the same length is, however, an entirely different matter. It can have high peaks; and to make the
matter worse, there is no simple method available to calculate the cross-correlation function
between two pseudorandom sequences except by brute force calculation and simulation. For long
sequences, this is not possible even with the fastest computers.
The cross correlation properties are as important in communication systems as
autocorrelation properties. Cross correlation is a measure of agreement between the two different
codes. The periodic cross correlation between any pair of m-sequences is very high. Such high
values of cross correlation are undesirable in CDMA communications. For CDMA applications,
m-sequences are not optimal. For CDMA, we need to construct a family of spreading sequences,
one for each which, in which the codes have well-defined cross-correlation properties. In general,
m-sequences do not satisfy the criterion. One popular set of sequences that does are the Gold
sequences. Gold sequences are attractive because only simple circuitry is needed to generate a
large number of unique codes.Gold sequences have been proposed by Gold in 1967 and 1968.
These are constructed by EXOR-ing two PN sequences of the same length with each other. Gold
developed new sequences with better cross correlation properties called Gold sequences. Gold
sequences are defined using a pair of preferred sequences. Gold sequences of length N can be
constructed from a preferred-pair of PN-sequences. This two PN sequences are XORed (modulo-2
addition) together to generate Gold code sequences. The result is a new period sequences with the
period N = 2 1n . To achieve increased capacity, at an expense of altering the correlation
properties slightly, a pair of m-sequences may be used to generate a set of Gold sequence, which
have the property that the cross-correlation is always equal to 1, when the phase offset is zero.
Non-zero phase offset produces a correlation value from one of the three possible values. In this
work a pair of specially selected m-sequences (where m = 5) is taken, and performing the modulo-
2 sum of the two sequences for each of the L=2n-1 cyclically shifted version of one sequence
relative to the other sequence.
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The Configuration for the generation of the Gold code sequences from the modulo 2
addition of two same length PN sequences as shown in figure 4.1.
Figure.4.1 Generation of the Gold Code sequences
Chapter 5: Simulation Results
5.1 Simulation results for PN sequences
Suppose the generator taps are 0 1 2 3 4[ , , , , ]g g g g g g = =[1 0 1 0 1] and the corresponding
generator polynomial is,2 4
( ) 1g D D D= + + then the result will be displayed as given bellow:
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Enter the size of the Linear Feedback Shift Register (LFSR) = 4
Initial State of the LFSR =
0 0 0 0
The generator (gm) =
1 0 1 0 1
Status of Register after the 1 clock is : 1 0 1 0
Status of Register after the 2 clock is : 0 1 0 1
Status of Register after the 3 clock is : 1 0 0 0
Status of Register after the 4 clock is : 0 1 0 0
Status of Register after the 5 clock is : 0 0 1 0
Status of Register after the 6 clock is : 0 0 0 1
Status of Register after the 7 clock is : 1 0 1 0
Status of Register after the 8 clock is : 0 1 0 1
Status of Register after the 9 clock is : 1 0 0 0
Status of Register after the 10 clock is : 0 1 0 0
Status of Register after the 11 clock is : 0 0 1 0
Status of Register after the 12 clock is : 0 0 0 1
Status of Register after the 13 clock is : 1 0 1 0
Status of Register after the 14 clock is : 0 1 0 1
Status of Register after the 15 clock is : 1 0 0 0
The number of bits in PN-sequence = 15
Generated PN-sequence is : 1 0 1 0 0 0 1 0 1 0 0 0 1 0 1
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0 5 10 150
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Figure 5.1 PN sequences(m-sequences) for N=4
0 2 0 0 4 0 0 6 0 0 8 0 0 1 0 0 0 1 2 0 00
0. 1
0. 2
0. 3
0. 4
0. 5
0. 6
0. 7
0. 8
0. 9
1
Figure 5.2 PN sequences(m-sequences) for N=10
The number of bits in PN-sequence = 1023
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5.2 Simulation Results for Gold Code Sequences
Suppose the first generator taps are 0 1 2 3 4[ , , , , ]g g g g g g = =[1 0 1 0 1] and the
corresponding generator polynomial is,2 4
( ) 1g D D D= + + . And second generator taps are
0 1 2 3 4[ , , , , ]g g g g g g = =[1 1 0 0 1] and the corresponding generator polynomial is,
1 4( ) 1g D D D= + + then the result will be displayed as given bellow:
Enter the size of the Linear Feedback Shift Register (LFSR)1 = 4
Enter the size of the Linear Feedback Shift Register (LFSR)2 = 4
Enter the first Generator polynomial = [1 0 1 0 1]Enter the second Generator polynomial = [1 1 0 0 1]
Status of Register after the 1 clock is : 1 0 1 0
Status of Register after the 2 clock is : 0 1 0 1
Status of Register after the 3 clock is : 1 0 0 0
Status of Register after the 4 clock is : 0 1 0 0
Status of Register after the 5 clock is : 0 0 1 0
Status of Register after the 6 clock is : 0 0 0 1
Status of Register after the 7 clock is : 1 0 1 0
Status of Register after the 8 clock is : 0 1 0 1
Status of Register after the 9 clock is : 1 0 0 0
Status of Register after the 10 clock is : 0 1 0 0
Status of Register after the 11 clock is : 0 0 1 0
Status of Register after the 12 clock is : 0 0 0 1
Status of Register after the 13 clock is : 1 0 1 0
Status of Register after the 14 clock is : 0 1 0 1
Status of Register after the 15 clock is : 1 0 0 0
The number of bits in PN1-sequence = 15
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Status of Register after the 1 clock is : 1 1 0 0
Status of Register after the 2 clock is : 0 1 1 0
Status of Register after the 3 clock is : 0 0 1 1
Status of Register after the 4 clock is : 1 1 0 1
Status of Register after the 5 clock is : 1 0 1 0
Status of Register after the 6 clock is : 0 1 0 1
Status of Register after the 7 clock is : 1 1 1 0
Status of Register after the 8 clock is : 0 1 1 1
Status of Register after the 9 clock is : 1 1 1 1
Status of Register after the 10 clock is : 1 0 1 1
Status of Register after the 11 clock is : 1 0 0 1
Status of Register after the 12 clock is : 1 0 0 0
Status of Register after the 13 clock is : 0 1 0 0
Status of Register after the 14 clock is : 0 0 1 0
Status of Register after the 15 clock is : 0 0 0 1
The number of bits in PN2-sequence = 15
Generated PN1-sequence is :
1 0 1 0 0 0 1 0 1 0 0 0 1 0 1
Generated PN2-sequence is :
1 0 0 1 1 0 1 0 1 1 1 1 0 0 0
Generated gold-sequence is :
0 0 1 1 1 0 0 0 0 1 1 1 1 0 1
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The simulation results for N=4
The first generator polynomial for PN sequence 1 is [1 0 0 1 0 1 1 0 0 0 1 ]
The first generator polynomial for PN sequence 2 is [1 1 0 0 0 0 1 0 1 0 1 ]
As shown in figure 5.3,the generated PN sequences 1 for N=4,the total number of bits in these
sequences are N= 2 1n =15 bits
As shown in figure 5.4,the generated PN sequences 2 for N=4,the total number of bits in these
sequences are N= 2 1n =15 bits.
As shown in figure 5.5,the generated Gold Code sequences for N=4,the total number of bits in
these sequences are N= 2 1n
=15 bits.These Gold code sequences aer generated by XORing thePN sequences 1 and PN sequences 2.
2 4 6 8 10 12 14-0.2
0
0.2
0.4
0.6
0.8
1
Generated m-sequence1 of length 2n1-1
Chip Index (k1)
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Figure 5.3 First PN Sequences for N=4
2 4 6 8 10 12 14-0.2
0
0.2
0.4
0.6
0.8
1
Generatedm-sequence2of length2 n2-1
ChipIndex(k2)
Figure 5.4 Second PN Sequences for N=4
2 4 6 8 10 12 14-0.2
0
0.2
0.4
0.6
0.8
1
Generatedgold-sequenceof length2 n2-1
ChipIndex (k)
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Figure 5.5 Generated Gold Code Sequences for N=4
The simulation results for N=10
The first generator polynomial for PN sequence 1 is [1 0 0 1 0 1 1 0 0 0 1 ]The first generator polynomial for PN sequence 2 is [1 1 0 0 0 0 1 0 1 0 1 ]
As shown in figure 5.6,the generated PN sequences 1 for N=10,the total number of bits in these
sequences are N= 2 1n =1023 bits
As shown in figure 5.7,the generated PN sequences 2 for N=10,the total number of bits in these
sequences are N= 2 1n =1023 bits.
As shown in figure 5.8,the generated Gold Code sequences for N=10,the total number of bits in
these sequences are N=2 1
n =1023 bits.These Gold code sequences aer generated by XORing the
PN sequences 1 and PN sequences 2.
100 200 300 400 500 600 700 800 900 1000-0.2
0
0.2
0.4
0.6
0.8
1
Generated m-sequence1 of length 2 n1-1
Chip Index (k1)
Figure 5.6 Generated PN Code 1 Sequences for N=10
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100 200 300 400 500 600 700 800 900 1000-0.2
0
0.2
0.4
0.6
0.8
1
Generatedm-sequence2of length2 n2-1
ChipIndex (k2)
Figure 5.7 Generated PN Code 2 Sequences for N=10
100 200 300 400 500 600 700 800 900 1000-0.2
0
0.2
0.4
0.6
0.8
1
Generated gold-sequence of length 2 n2-1
Chip Index (k)
Figure 5.8 Generated Gold Code Sequences for N=10
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5.3 Conclusion
From the above results and Graphs we can safely conclude the following :
1) I have successfully generated a PN sequences and Gold Code sequences. We can generate PN
sequences and Gold Code sequences of any bit length and modulate a message signal. This signal
is called spreaded signal. We have also successfully demodulate the spreaded signal using the same
Gold Code sequence to produce the original message signal.
2) Better Auto correlation of the Gold Codes over the PN sequences, thus proving that Gold Code
is more suitable for modulation and spreading of a message signal than the Pseudo Noise
sequences.
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REFERENCES
[1] Raymond L. Pickholtz, Donald L. Schilling, Laurence B. Milstein. Theory of Spread
Spectrum Communications -- A Tutorial, IEEE Transactions on Communications, Vol. COM-
30, May 1982, pp. 855-884.
[2] Robert C. Dixon. Spread Spectrum Communications, Second Edition, John Wiley and Sons,
New York, 1984.
[3] Edward A. Lee, David G. Messerchmitt, Digital Communications, Second Edition, Kluwer
Academic Publishers, USA, 1994.
[4] Marcus C. Wlden, Roger D. Pollard. On the Processing Gain and Pulse Compression Ratio of
Frequency Hopping Spread Spectrum Waveforms, IEEE National Telesystems Conference
Proceedings, 1993, pp. 215-219.
[5] T.S.D. Tsui, T.G. Clarkson. Spread Spectrum Communication Techniques, Electronics and
Communication Engineering Journal, Februaru 1994.
[6] Laurence B. Milstein, Donal L. Schilling. The Effect of Frequency-Selective Fading on a
Noncoherent FH-FSK System Operating with partial Band Tone Interference, IEEE
Transactions on Communications, Vol. COM-30, May 1982, pp. 904-912.
[7] G. Mandyam and J. Lai, Third- Generation cdma systems for enhanced data services,
Academic Press, 2002.
[8] B. Lee, B. Kim, Scrambling Techniques for CDMA Communications, New York Kluwer
Academic Publishers, 2002.
[9] http://en.wikipedia.org/wiki/Pseudorandom_binary_sequencehttp://
micromouse.cannock.ac.uk
[10] http://en.wikipedia.org/wiki/DSSS
[11] www.mathworks.com/
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APPENDIX
Abbreviations:
AMPS analog advanced mobile phone system
N-AMPS narrowband AMPS
D-AMPS digital AMPS
EDGE Enhanced Data Rates for GSM Evolution
TIA telecommunications industry association
CDMA code division multiple access
DS direct sequence
ERBF radial basis function with Euclidean distance measure
ETSI European Telecommunications Standards Institute
FDMA frequency division multiple access
FECC forward error correction coding
FH frequency hopping
GSM Global System for Mobile
IMT 2000 International Mobile Telecommunications 2000
ICI inter chip interference
ISI inter symbol interference
IS-95 interim standard-95
ITU International Telecommunication Union
MSC mobile switching centre
MUD multiuser detector
PG processing gain
PN pseudo-noise or pseudo-random
SS spread spectrum
TDMA time division multiple access
TH time hopping
UMTS Universal Mobile Telecommunication Standard
WCDMA wideband CDMA